Question

A plane traveled 1463 miles to Moscow and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 19 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answer 1

The speed of plane is 105 miles per hour and speed of wind is 28 miles per hour.

Step-by-step explanation:

Given,

The distance traveled by plane = 1463 miles

The trip with the wind took 11 hours.

The trip took 19 hours against the wind.

Let,

s be the speed of plane and w be the speed of wind.

Therefore;

Speed with the wind = s+w

Speed into the wind = s-w

We know that;

Distance = Speed * Time

Therefore;

Equation for trip taken with wind.

1463 = 11(s+w)

Dividing both sides by 11

$\frac{1463}{11}=\frac{11(s+w)}{11}\\133=s+w\\s+w=133\ \ \ Eqn\ 1$

Equation for trip taken into the wind

1463 = 19(s-w)

Dividing both sides by 19

$\frac{1463}{19}=\frac{19(s-w)}{19}\\77=s-w\\s-w=77 \ \ \ Eqn\ 2$

Adding Eqn 1 and 2

$(s+w)+(s-w)=133+77\\s+w+s-w=210\\2s=210$

Dividing both sides by 2

$\frac{2s}{2}=\frac{210}{2}\\s=105$

Putting s=105 in Eqn 1

$105+w=133\\w=133-105\\w=28$

The speed of plane is 105 miles per hour and speed of wind is 28 miles per hour.